How to add tag for integration list

There is no setting for that, but you can do it with some custom code.
Here is an example:
https://github.com/ibericode/mc4wp-snippets/blob/master/integrations/subscriber-tags.php

And here is how to specify what specific integration it should work on:
https://github.com/ibericode/mc4wp-snippets/blob/master/integrations/integration-slugs.md

Hope that helps. If you have any questions, please let me know!